The lottery is often used as an example of extreme irrationality. And it seems so obvious that the opinion is pretty pervasive across the board, probably even in people who are not particularly skeptical towards other aspects of life. My friend calls the lottery a “tax on people who can’t do math” and this seems to be a popular saying.
But then there is the counterclaim made by some to justify the idea of playing the lottery. You’re supposed to be buying hope. For $2.20 per 2 games (having just checked the price in my home state), you’re buying yourself the fantasy of winning, and isn’t that worth $2.20?
Well, for starters, I agree with the argument given in this LessWrong post that even this kind of approach is a dire waste of hope, and of the emotional energy that’s invested in the act of hope. On my part, I think that donating that $2.20 a week to a successful organisation will save a person’s life after about 4-5 years. And though our reptilian brain may not get the same zap of pleasure reward from contemplating this (as opposed to how you can be swimming in gold coins), it’s hope that’s many, many orders of magnitude more real than the lottery kind of hope. Plus of course most people probably play more than 1 game at a time which cuts down the time needed to save a life considerably.
Which brings me to the point of the post: how you should be playing if you think it’s still worth it for the sake of hope. Here’s the system I thought up recently — play as many games as you want but you can only pick consecutive numbers. So for a 7 number game system, you can play 1, 2, 3, 4, 5, 6, 7 or 12, 13, 14, 15, 16, 17, 18 and so on.
Now how does that alter any hope? I think this shows the cognitive bias lotteries are exposing (other than just lack of calculation). It feels ridiculous to play 1, 2, 3, 4, 5, 6, 7 — of course THAT one will never come up! That’s the problem, because these combinations seem special even our reptilian brain can see how stupidly rare they are. But for a pattern of numbers that you picked yourself, it feels like it’s got higher odds. And the funny thing is even if you know intellectually that the odds of your favourite numbers coming up are exactly the same as 1, 2, 3, 4, 5, 6, 7, the supposed lack of pattern in YOUR pick can fool your reptilian brain.
So it seems that sometimes our irrationalities can be overcome by using some kind of hack that will get our minds to look at a similar case that we’re less susceptible to. Maybe you have another example where this can be done? Bottom line, I don’t mind anymore that people play the lottery as long as they acknowledge that they might as well be playing 1, 2, 3, 4, 5, 6, 7. I’ll end with a rational koan on lotteries also from LessWrong:
Two students of Bayes were walking to the dojo one morning, and when they passed a newsagent, the senior of the two said to his friend “hold on a mo”, and went in and bought a lottery ticket. As they continued their walk the junior student was frowning, and he went red with mental effort, and finally at the dojo gates he accosted his friend and said “I’ve been thinking and thinking and I can’t see why the hell you bought that ticket. You know they’re useless. I know you’re not mad. Now I’m going mad. Explain yourself!”. The older student cracked up laughing, and said “I have received what I paid for”, before throwing the ticket in the bin and proceeding into class. The younger student was enlightened. [Source]
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“I have received what I paid for�, before throwing the ticket in the bin and proceeding into class. The younger student was enlightened.
…unfortunately, that ticket turned out to be the winner for the $267 million dollar Powerball jackpot.
Playing consecutive numbers, or numbers 31 and under, have a much lower payout than higher numbers because people statistically pick patterns, birthdays and other dates that are important. Should those numbers come up you are statistically likely to both share the jackpot and share with a greater number of people.
Also, studies in the UK show that the lowest jackpot prize would be for 1,2,3,4,5,6 as approx. 15,000 people play those numbers each week.
However, by your logic, when there is a massive rollover it is illogical NOT to play the lottery as your expected return is greater than 0.
Back in the logical world though, the lottery is a reverse insurance. You pay an insignificant premium to cover a very small probability that you win. The money spent is not missed and hence there is no real downside but a potentially massive upside, with a 1 in 50 chance of an actual prize.
The only valid point you made is that there are many better uses for the money, but so what? We waste money all the time. Not every decision is economically, or morally, optimal.
- Economist, gambler and lottery player.
Oops, forgot to respond. But before I do, just wondering if you’re a minority opinion amongst fellow economists (that it’s rational to play the lottery) or is this the consensus?
Definitely not the majority opinion. It is a negative return on your stake long term, but as is often said, in the long run we’re all dead.
Besides, I have no plans on having children so leaving a single penny after my death is a waste. I’d rather spend/waste a tiny, unmissable, proportion of my income regularly now than have a meaningless sum to spend when I retire, assuming I had saved for retirement.
Obviously your point about using the money charitably is much more poignant, but have we not seen where ill-researched charitable giving leads? T-Shirts for Africa being one of my favourites – http://1millionshirts.org/ as well as your post on the badly run charities that grow and reduce donations to more efficient and effective ones.
But then if you actually hope to win won’t that just increase the meaningless sum further?
Also I don’t really buy the argument about charities since the fact that in most cases your money will be wasted is no different to investing in a for-profit business, there are certainly charities out there that are provably excellent at delivering improvement-value for money. Maybe I should actually post about this — it might be that psychologically criticism of systemic problems in the aid sector might just result in us subconsciously using it as an excuse to simply reduce donations which in the long run could well reduce certain factors.
On the lottery, you’re right, I did not consider multiple people betting on 1, 2, 3, 4, 5, 6, 7. But then consider a modified version of the scenario — if you were playing a lottery where everyone’s combination had to be unique and you were the first one so had a pick of all combinations then my argument still stands, if you’re fine with playing at all you should then be fine with playing 1..7
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